Based on the identities of participants in battles after Endor, the Alliance remained as such for a while, but officially became the Republic shortly before Jakku happened 1 year after Endor, and the treaty was signed as an effective surrender by the Empire soon after. The founders of the FO jumped at the same time the treaty was signed, so one could say all these events are together in the same year or so. Leia left the Republic decades later (but no idea specifically when) when the FO made their appearance from hiding - to form the Resistance.
– thegreatjediJan 14 '16 at 5:57

5

" When the Empire became the New Republic" this is either the most imprecise retelling of the back story ever, or a deep allegory... ;)
– DVK-on-Ahch-ToJan 14 '16 at 12:47

@DVK - I'm talking about the real estate of the empire, not the Imperial hierarchy.
– Wad CheberJan 14 '16 at 23:34

2 Answers
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The canon novels "Star Wars: Aftermath", "Lost Stars", and "Before the Awakening" fills in some of these gaps, as well as Visual Dictionary from "The Force Awakens".

In Aftermath, it is mentioned that a small Senate, with Mon Mothma as Chancellor, is formed and begins meeting around 6 months after the Battle of Endor. This new government is called the New Republic.

After the Battle of Jakku (a year and four days after The Battle of Endor), the Galatic Concordance, a peace treaty between the New Republic and the remnants of the Empire is signed. This treaty establishes the territory of both the Republic and Empire, as well as a "neutral zone" in between both governments. The First Order mostly controls the Unknown Regions, where the Emperor had previously sent scouts and scientists attempting to discover the origin of the Dark Side of the Force.

It is unclear as to when exactly the remnants of the Empire named themselves as "The First Order."

The Resistance is formed as a guerrilla group when the The First Order begins attacking Republic outposts. The Republic does not believe The First Order is a threat, so a small group is formed to resist what they believe is a clear and present danger. While it is never stated, it is heavily implied that this began shortly after the massacre at Luke's Jedi Academy.

Do the books give a timeline (at least in reference to TFA) when the attack on the Academy took place?
– Dave JohnsonJan 14 '16 at 14:31

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No. Aftermath takes place 6 months after Endor. Lost Stars takes place over the course of The Original Trilogy up until The Battle of Jakku. Before the Awakening has three short stories -- one each for Poe, Finn, and Rey -- which take place basically within a year of when The Force Awakens occurs. Before the Awakening does not give any information on the attack on the Academy. I suspect the new novel "New Republic: Bloodline" (to be published in May 2016) might provide more information on that topic.
– scott.korinJan 14 '16 at 14:34

Events mentioned in the question:

When was the Empire considered defeated?

Shortly after the Empire's crushing defeat at the Battle of Jakku, in 5 ABY, when most of the remnants of the Imperial leadership surrendered.

When did the Empire become the New Republic?

The New Republic was founded in 4 ABY, just after the Emperor was killed, but grew slowly at first. By the end of its first year, it could be described as follows (by Imperial sympathizers):

...with two Death Stars gone, a significant portion of the Empire’s best and brightest were snuffed out, too. The New Republic seized that opportunity. The Rebellion was gone, and a new government grew swiftly — if clumsily — in its place...

Sloane can see the territorial divisions, and it makes it easy to identify as the present state of political unrest. The galaxy has been butchered and stitched back together into an ugly quilt. Some systems have gone over to the New Republic, with just as many separating into their own fiefdoms.
- Star Wars: Aftermath: Life Debt

When did the Rebel Alliance become the Resistance?

It didn't directly become the Resistance, but the Resistance was modeled on the Rebel Alliance, and included some important figures from the Rebellion. It was created in 30 ABY, 6 years before the events of The Force Awakens1.

The Alliance had presumably ceased to exist as such at least 20 years earlier, when the Empire was essentially wiped out and the New Republic was able to defend itself from the remnants of the Imperial forces.

When Leia walked inside, she saw that everyone she’d contacted was already there; she’d been early, but they came even earlier. In the back were those who had traveled farthest to help her — Nien Nunb, Ematt, and even Admiral Ackbar, standing straight, ready to serve.

To the side was Harter Kalonia, who hadn’t hesitated to accept Leia’s invitation, and thank goodness; it was always good to have a doctor on hand who knew how to keep a secret. Clustered closer were the young pilots she’d recruited, chosen from either those she had worked with personally— such as Joph Seastriker, who stood at the very front — or those Joph and the other pilots had vouched for, such as Snap Wexley and Zari Bangel...

“The sun is setting on the New Republic,” Leia said. “It’s time for the Resistance to rise.”
- Star Wars: Bloodline

When was the First Order established?

It was already being planned by 30 ABY, 6 years before the events of The Force Awakens:

Lady Carise could have sneered. “Yes. Because I do not speak for myself alone, Hadrassian. Or have you forgotten your loyalties? Do you no longer wish to restore what we lost with the Empire? Have you abandoned the First Order completely?”

Never before had Lady Carise spoken those words out loud in her office. The First Order. Someday, the entire galaxy would shout them with pride, but for now they were too secret, too sacred, to be taken lightly. That dream was so close to becoming reality — only a few years away, if even that — and protecting it required discretion.
- Star War: Bloodline

But it hadn't yet emerged as a real entity. That would take another year or so1:

They needed a firm structure before proceeding. But soon, the Centrist worlds would leave the New Republic, tearing themselves from the mire of the Senate’s inaction to create and support the First Order. Her heart sang merely thinking of it.
- Star Wars: Bloodline

Other important events:

When did Leia marry Han?

Leia and Han were married on Endor, immediately after the Battle of Endor:

Norra says: “I didn’t realize you two were married.”

“It was right there on the Endor moon after everything. We had a small ceremony, just those we trust. We don’t keep it secret, but we didn’t make it public, either.”
- Star Wars: Aftermath: Life Debt

When was Ben born?

By the end of 4 ABY, Leia was pregnant:

“Solo and Princess Leia.”

“Oh.”

Sinjir claps his hands. “Bonus trivia: She’s pregnant.”

A chorus of retorts and refutations rise in response. But Sinjir crosses his arms and jeers at them. “What? Don’t look at me like I’m some malfunctioning protocol droid spitting babble. Whatever your jobs are, mine is to read people like they’re a menu at the local automat. The way she dresses? The way she carries herself? The rosy flush to her cheeks? Her hands drifting unconsciously to her stomach? Preg-nant.” That last word he says in a sing-songy way.

“PREEEEG-NAAAANT,” Mister Bones echoes, also singing— except his song is a disharmonic glitch ballad. Everyone winces.

“Stop,” Sinjir tells the droid.

“ROGER-ROGER.”
- Star Wars: Aftermath: Life Debt

And:

Her mind is a tangle of thoughts. The complexities of politics, the love of (and anger over) Han, the loss of Luke, and above all else the ever-persistent worry about the life she carries...
- Star Wars: Aftermath: Life Debt

1This means - somewhat surprisingly - that the Resistance actually predates the First Order, at least officially, by several months.